Laminated glass structures may be used as components in the fabrication of various appliances, automobile components and architectural structures or electronic devices. For example, laminated glass structures may be incorporated as cover glass for various end products such as refrigerators, backsplashes, decorative glazing or televisions. However, it may be difficult to cut or otherwise shape the laminated glass structures using machining methods typically used in manufacturing environments without causing fractures in the glass layer given limitations of the machining methods that might be used and properties of the laminated glass structures. For example, many such machining methods are not used to cut glass, plastic or adhesives. Accordingly, there is a need for methods of shaping laminated glass structures that minimize effort and cost of glass laminate use and installation.